\[ \left (e^{2 x}-v^2\right ) y(x)+y''(x)=0 \] ✓ Mathematica : cpu = 0.0189899 (sec), leaf count = 46
\[\left \{\left \{y(x)\to c_1 \Gamma (1-v) J_{-v}\left (\sqrt {e^{2 x}}\right )+c_2 \Gamma (v+1) J_v\left (\sqrt {e^{2 x}}\right )\right \}\right \}\] ✓ Maple : cpu = 0.042 (sec), leaf count = 17
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\sl J}_{v}\left ({{\rm e}^{x}}\right )}+{\it \_C2}\,{{\sl Y}_{v}\left ({{\rm e}^{x}}\right )} \right \} \]